Blog Roll: Russia

 

Dec 29, 2025. Russia Threatens to Toughen Its Stance on Ending the War in Ukraine In a somewhat bizarre sequence of events, the US President (Donald Trump) had a phone call with the Russian President (Vladimir Putin), had a meeting with the Ukrainian President, Volodymyr Zalenskyy, and then had another call with Vladimir Putin. Without getting into the weird timing and details of these events (Was Trump getting Instructions from Putin? Was Putin looking for a pretext to continue fighting, etc. etc.), it seems that the peace process is in a "stalling mode" and the battlefield has settled into a stalemate. Why is this?

My state space statistical model of the Russian economy is also very unusual compared to other countries in the World-System. The RUL20 model is unstable and highly cyclical, forecast to peak again around 2050 and then collapse (again) after that. In other words, if Ukraine can hold out until 2050, the Russian Empire would collapse again as a results of it's own internal dynamics. But, 25 years is a long time.

Another interesting aspect of the RUL20 model is that the best Geopolitical Alignment for Russia would be for the country to join the European Union (!). Again, maybe the passing of a quarter century would be necessary for that to happen.

Here is a Blog Roll of my postings on Russia:

• Five Futures for Russia Joining the EU provides the best future for Russia!
• Geopolitical Futures for Ukraine Alignment with Russia is positive if cyclical but the best model is Business-As-Usual (no Geopolitical Alignment).
• A New Axis of Evil? Geopolitical alignment of Russia, India and China do not produce attractive model forecasts for any of the countries.
• Futures of Syria Geopolitical Alignment with Russia is OK, but Business-as-usual (no Geopolitical Alignment) is best.
• Hegemonic Dominance Forecasts for the World System  In terms of unending, uncontrolled exponential growth, alignment with Russia would be best but the environmental consequences would be quite negative.
• Futures for China Alignment with Russia would produced uncontrolled, unending exponential growth that would have negative environmental consequences.
• US Attempts to Dominate India Geopolitical Alignment with Russia  would produce a strongly cyclical future for India with large growth and collapse cycles.
• Seven Futures For Iran Geopolitical alignment with Russia would produce collapse.
• Futures for the World System Dominance by Russia would produce strong cycles of growth and collapse.
• Futures for Argentina Alignment with Russia produces unending, uncontrolled exponential growth and an environmental nightmare.
• Latin American Forecasts Alignment with Russia would produce immediate collapse.
• Forecasts for Columbia Alignment with Russia would produce wild cycles of growth and collapse.
• Futures for Germany Alignment with Russia would produces unstable cycles of growth and collapse.

Continuing Imperialist alignments with Russia do not produce attractive outcomes, but unending and uncontrolled exponential growth will be an attractive future for some political-economic elites.

Notes

Wikipedia

Economy of Russia

Shadow Economy of Russia

Economic History of the Russian Federation

Economic History of the Russian Empire

Corruption in Russia

Economy of Ukraine

History of Russia

Russian Empire

Russo-Ukrainian War

Blog Roll: The Great Depression

 

The Great Depression of the Early 20th Century is (and was) a systemic event between World War I and World War II that has been intensely analyzed, if over-analyzed (see References below). The one viewpoint that seems to have been under-analyzed is the perspective of Systems Theory. The following is a Blog Roll of my postings on the topic:

• How do we define Great Depressions? From the standpoint of Systems Theory, not correctly.
• Shock Theories of Great Depressions An obvious but inadequate perspective.
• Did the Great Depression hit at a conjuncture of Technological Change? Maybe, but there have been a lot of Technological Long Waves and Conjunctures.
• Measuring the Great Depression Obsessive focus on the collapse of Gross Domestic product is myopic. 
• The Minsky-Kindleberger Framework So far, the best qualitative systemic framework. It needs to be tested.
• War and Normalcy: (1914-1929)  The Roaring Twenties Bubble was "popped" by the 1929 Stock Market Crash after which the US Economy returned to the long-run attractor path.
• Forecasting the Great Depression in France Not easy (or maybe even possible) since France reinvented itself after WWI and responded very conservatively to the shocks of the Great Depression.

Systems Theory opens up an entirely new perspective on the Great Depression. I will keep adding posts to this Blog Roll until I think I've attacked all the issues and competing explanations.

Notes

Readings

• Peter Fearon (1987) War, Prosperity and Depression, The US Economy 1917-1945. A good summary of the Economic Thinking on the Great Depression
• Charles Kindleberger (2013) World in Depression, 1929-1939 The best understanding of the Great Depression as a World-wide, Systemic Event
• Charles Kindleberger (2015) Manias, Panics and Crashes: A History of Financial Crises What causes departures from the Attractor Path 
• US Government (2008) Outline of US History, Chapter 10, War, Prosperity and Depression. The "official" history for the US! 
• Immanuel Wallerstein (2004) World-Systems Analysis: An Introduction
• Ludwig von Bertalanffy (2015) General System Theory: Foundations, Development, Applications Kindle Edition

Blog Roll: Latin America

 

January 3, 2026. TRUMP INVADES VENEZUELA The New York Times is providing live updates here.

Dec 2025. The Trump Administration has resurrected the Monroe Doctrine and added a Trump "Corollary". What effects might be expected from carving the World-System up into Spheres of Influence? Here's a Blog Roll of my postings on Latin America:

• Latin America and the Donroe Doctrine Will the Trump "Corollary" to the Monroe Doctrine help Latin America? Unlikely.
  
• Six Futures for Growth of Colombia The most stable Future for Colombia focuses on Globalization. The Colombian BAU model exhibits unstable cycles.
• Growth Forecasts for Venezuela  The best future for Venezuela focuses on Technical Efficiency (not Technical Productivity). For the entire economy, Venezuela is approaching a Steady State. The best controller for Inflation in Venezuela is Globalization.
• Latin American Futures The best future for Latin America is Business-as-Usual (no Geopolitical Alignments). However, the Latin America BAU model is unstable and cyclical.
• Geopolitical Linkages: Canada, Mexico and the US Trade Wars between CA, MX and the US will benefit none of the countries.
• Future Forecasts for the EU The best forecast is to pursue Business-as-Usual with no Geopolitical Alignments.
• Latin American Geopolitical Alignment with China would benefit Latin America but would be resisted by the US.
• Future Forecasts for Argentina Business-as-Usual and Geopolitical Alignment with Russia produce uncontrolled, unstable exponential growth. Growth in Government Expenditure is out of control. Should Argentina take a Random Walk with Shock Therapy? Better System Control is needed in Argentina rather than Shock Therapy. Linking with the Latin American Regional Economy would provide a stable future growth path for Argentina; linking with the US would produce Growth-and-Collapse. Historically, the Economy of Argentina has been through many Economic Bubbles as a result of Political Mismanagement.
• Futures for Growth of Mexico Business-as-Usual and focus on Technical Productivity produce stable growth. Geopolitical Linkage with the World System, the US and China produce Collapse.
  

Blog Roll: The United Kingdom (1950-2000+)

 

After Leaving the European Union on on 31 January 2020 (Brexit), Britain's future remains murky. ChatGPT reports that:

ChatGPT also provides a number of background references for this conclusion:

• UK Economy returns to growth, but only just, as Reeves plans budget
• Bank of England Monetary Policy Report -- November 2025
• UK Inflation, OBR 2026 Forecasts
• IFS Economic Outlook for the UK: navigating narrow paths
• IMF: Bank of England Should be 'Very Cautious'

If you are interested in forming your own opinions about the Economy of the United Kingdom, here is a Blog Roll of results from various historical Systems models:

• Six Forecasts for the United Kingdom Some are stable, some are not.
• Technological Change in the United Kingdom Technical Productivity seems to be reaching a Steady State in the UK.
• Should Great Britain Have Exited the European Union? A Great Counterfactual!
• Is the UK Economy Heading for a Steady State? Maybe and maybe not!
• Hegemonic Dominance Not surprisingly, the UK is one of "also rans" in the battle for Hegemonic Dominance of the World System, but that is not necessarily a good thing.

The Economy of the United Kingdom in History:

• The UKL19D Model Collapsing Economy, unstable Export-Urban Population controller.
• The UKE20 Model During the Great Depression, the UK had doubly unstable Growth-Export and Export-Employment Controllers.
• The UKL19 Model During the Late 19th Century, the British economy was unstable and collapsing due to an unstable Urban-Export controller.
• The UK18 Model During the 18th Century, the British Economy was also unstable and collapsing due to an unstable Growth-Export Controller and an Unstable Export-Population Controller. Historically, the UK Economy was saved by the Industrial Revolution.
• The UK17 Model During the 17th Century, the British Economy had an unstable Growth-Exports controller and an unstable Malthusian-Export controller (Exports allowing the economy to growth exponentially.
• The UK16 Model During the 16th Century, the British Economy had an unstable Growth-Export controller and an unstable Urban-Population-Export controller, allowing the economy to growth exponentially.

Technology Long Waves

  

The Kondratiev Wave is an important element of World-Systems Theory. The graphic above is taken from Andreas Goldschmidt and gives historical specifics for technological cycles. Goldschmidt's formulation allows for the idea to be tested (one of the models I always test), is partially consistent with economic Growth theory (particularly if we do not assume a functional form for exogenous disembodied technological change in the Solow-Swan Model) and I can present some examples.

• The Iranian Economy prior to 1979 and associated Tech Bubble.

Back-of-the-envelope Calculations: Global Warming

In the introductory chapter of  The Demon Haunted World: Science as a candle in the Dark Carl Sagan writes:

It was from [G. P.] Kuiper that I first got a feeling for what is called a back-of--the-envelope calculation: A possible explanation to a problem occurs to you, you pull out an old envelope, appeal to your knowledge of fundamental physics, scribble a few approximate equations on the envelope, substitute in likely numerical values, and see if your answer comes anywhere near explaining your problem. If not, you look for a different explanation, It cut through nonsense like a knife through butter.

Given the controversies that are currently swirling around Climate change (the President of the United States has called it a "hoax"), it would be useful for the non-scientists to have a back-of-the-envelope calculation to "cut through nonsense". There is a simple equation, called the Kaya Identity that would be very useful to understand.

I first became aware of the Kaya Identity on one of the first IPCC reports. The Kaya Identity proves a back-of-the-envelope way to calculate global temperature increase, T, from population growth. The current IPPC report, AR15, doesn't mention it in the introduction but it should. AR15 claims that it is already too late to limit anthropogenic (human caused) climate change. It is  dire warning but how can the non-scientists check the assertion. Let's work through he Kaya identity slowly and see what the calculations tell us.

The first step in the causal chain is the effect of population growth, N,  on economic production, Q. The Kaya equation is Q = qN where q is output per capita. In the Kaya framework, q is called an intensive variable while N and Q are extensive variables.

Blog Roll: The World System (1950-2000+)

 

The World System, typically used by the IPCC to model Global Climate Change, means one system explaining environmental and economic trends of the World. The World-System (notice the hyphen), a term used by World-Systems Theory, refers to a "World of Systems" in which nation states and regions form hierarchical Geopolitical relationships.

Here are some postings I have done from the perspective of both the World System and the World-System:

• Global Temperature Projections Using the World System model, Global Temperature will peak below +1.5 degrees Centigrade. Using the Kaya Model, it will not (goodbye Polar Ice Caps).
• A More Conservative Peak Oil Forecast World Oil production, and the resulting CO2 emissions, might not collapse in 2040.
• Peak Oil and Global Warming Peak Oil Production, at some time in the Future, seems reasonable but "when" is hard to predict.
• World Population Collapse Both the UN and my WL20 model predict that World Population will start to collapse after 2050. If that really happens, there will be ripple effects throughout the Kaya Identity!
• A New Axis of Evil Looks scary but they might be no better at running the World-System than the US.
• Geopolitical Linkages: Canada, Mexico and the US The Trump II Administration is tinkering with a World-System that they do not understand.
• US Attempts to Dominate India In the long-run, it would lead to the collapse of India.
• World System Steady State and Collapse The only stable, steady state future for the World System is dominance by Europe. Right now, competition between the major Hegemonic contenders (the US, Russia and China) might not produce a steady-state Future.
• Hegemonic Dominance Forecasts Dominance of the World System by Russia would lead to (1) unending exponential growth and (2) a Dystopian Nightmare.
• Six Futures for the World System The best Future for the World System involves no Hegemonic Leader.
• US CO2 Forecasts Emissions are declining in the US but the best way to reinforce the trend is to let gasoline prices increase, a political non-starter.
• Coal will make Reducing Energy Intensity Difficult Reducing the mining and burning of coal will be difficult and the Trump II Administration is trying to "Greenwash" the problem by rebranding it "Clean Coal," which it isn't.
• EU Gives Up on Climate Regulation! Really? Backtracking might simply be an admission that EU countries are reaching a steady state.
• US CO2 Emission Reduction Unlikely as a result of COP17 Steady-state emissions are more likely rather than reductions.
• World Impact Forecasts More on Impact Models, if you are interested. Impact models do not have feedback effects but they are easy to calculate by hand and maybe feedback effects are weak in the World-System.
• How to Balance the World System Wait for Growth-and-Collapse.

Some of the State Space Dynamic Components models (see the Boiler Plate) for the period 1950-2000+ are available as R-code and can be run here.

Blog Roll: Argentina

 Wikipedia notes (here) that:

Argentina's economy has swung from one of the world's richest in the early 20th century to repeated cycles of boom, bust, and hyperinflation, driven by commodity dependence, political instability, and policy shifts.

The newest shock to the economy has come from president Javier Milei's  Economic Austerity policies which have, evidently, failed and required a $20 Bailout from the Trump II Administration. 

I have a systems model (ARL20) of the Argentine Economy which can be used to investigate (1) the Late 20th and early 21st century Economic History of Argentina and (2) alternative Geopolitical Futures for Argentina and the resulting economic impacts.

• Seven Futures for Argentina Alignment with the US produces Growth-and-Collapse.
• The Bubbly Economy of Argentina Not a pretty picture.
• Latin American Futures Emphasis on Business-as-usual and Technological change provide the most likely futures.

You can experiment yourself with the ARL20 BAU model here.

Blog Roll: European Union

 

LeMonde reported, at the end of 2025, that Europe had become the largest supplier of arms to Ukraine, although the armaments were largely purchased from the US. And, in 2026 the EU and South America agreed to form a Free-Trade Zone with 700 million people. EU policy now seems to be a reaction to Geopolitical actions (and inactions) by the Trump II Administrations. From the graphic above (from ChatGPT), Security is not the only problem facing the EU.

I have a number of posts on the EU, but there is much more to analyze in the future:

• Was the EU economy Wrecked by Austerity? Around the turn of the 21st Century, the EU tried to break away from a stable attractor path for growth. They failed. Poor performance of the EU is simply a return to more moderate, sustainable growth.
• Is the EU Heading for a Steady State Economy? My forecasting models predict that a steady state provides the most likely future attractor path. Google AI doesn't think so.
• Was it a mistake for Britain to enter the EU? The typical question asked right now is whether Britain should have exited the EU (Brexit). However, the period after the Maastricht Treaty (1992) that founded the EU was a period of unsustainable growth that eventually returned Britain to the attractor path around 2010. A decade of "poor" growth before Brexit in 2020 was simply a return to the attractor growth path, not failure.
• Is Another EU Recession Likely? Yes, if growth exceeds the attractor path.
• Has the EU Given up on Climate Change? Evidently, the EU decided in 2020 to give up "fixed climate targets". However, CO2 emissions are forecast to decline well after 2040.
• Future Geopolitical Alignment Forecasts for the EU also suggest approach of the Steady State. Some geopolitical alignments (with the US and the World System) predict collapse of the EU. The best forecast, although it is not for unlimited exponential growth, is for  Business-as-Usual (BAU).
• How does the EUL20 BAU Steady-State Economy Model work? Not in ways that are envisioned by Modern Economic Theory but that are easily explained by Systems Theory.

Notes

You can run the EU_L20 Model (here) along with a number of other models for EU Countries. Explanations for data sources and how the models were constructed can be found in the Boiler Plate.

 

Wikipedia

• European Union (EU)
• Brexit
• Maastricht Treaty (1992)
• Steady State Economy
• Economy of the European Union
• History of the European Union
• Politics of the European Union
• Council of the European Union 
• Institutions of the European Union

The biggest Security problem facing the EU is Russian Expansionism. For more background, see my Blog Roll: Russia. The Russian Economy is highly cyclical and might well collapse (again) in the next few decades. However, integration of Ukraine in the EU will remain a problem as long as Russian Expansionism continues (see my Blog Roll: Ukraine).

Will the UK decide to return to the EU? See whether my Blog Roll: UK will help you make a forecast.

Do you think the EU-LA Free Trade Zone will help either the EU or Latin America? See my Blog Roll: Latin America.

EU_L20 Measurement Model

Three components in the EU_L20 state space explain 99.6% of the variation in the indicator variables: EU1 = (Overall Growth), EU2 = (CO2 - LU) an Environmental-Unemployment Controller and EU3 = (LU - Q) an (Unemployment - GDP) controller.

EU_L20 BAU System Matrix

The EU_L20 System Matrix is stable, meaning that the system will eventually reach a steady state.

Blog Roll: Venezuela

Jan 3, 2026. TRUMP INVADES VENEZUELA The New York Times is providing live updates here. My models (e.g., the VEL20 model, Latin American Regional Models and links below) suggest that the invasion and the aftermath (Trump claims the US will run the country) will not end well and are not in the best interests of Venezuela.

October 2025. Venezuela is currently in the News because the US appears to be planning an invasion of the country. Wikipedia notes (here) that "With the turn of the 21st century, the Venezuelan economy has been in a state of total collapse since 2013."

Here are some background forecasts from my VEL20 model and a model of the Latin American Region: 

• Eight Growth forecasts for Venezuela Maybe not surprisingly, the best growth options involve no Geopolitical Alignments for the country. Alignment with the US is worse than a Random Walk.
• Inflation in Venezuela The best option to control inflation, maybe in this case surprisingly, is to increase Globalization.
• Venezuela Growth Forecast Without external interference (for example, a US invasion), the Venezuelan economy is predicted to reach a steady state after 2100.
• Latin American Futures Latin American has a somewhat different future from Venezuela, but Geopolitical Alignment with the Latin American region is another policy option for Venezuela.
• How will US Military Action affect the Economy of Venezuela? Not well!

Activities within Latin American and within the MAGA movement suggest that events in Venezuela and in the US are changing quickly and cannot be easily predicted. Hopefully, historical models and forecasts will make events that happen in the future somewhat more understandable.

You can experiment yourself with the VE20 model using an R-code simulation (here). To understand how the statistical models are created and estimated, see the Boiler Plate. 

Exercise: How will the negative shock of invasion affect the state of the country (see the last line of code in the VE20 model)?

 Background

• Proposed Invasion of Venezuela 
• US 2025 National Security Strategy particularly the revival of the Monroe Doctrine
• Crisis in Venezuela
• Economy of Venezuela
• Economic History of Venezuela
• Google AI

Malthusian Crisis in Ethiopia?

 

Wasn't Malthus Wrong?

The PBS NewsHour is reporting (here) that "millions ... [in Ethiopia] ... still face the risk of starvation as a result of drought conditions", even though the Civil War ended in November, 2022. The last time Ethiopia faced famine was in 1984. Last March, the World Food Program and the USAID suspended food deliveries because grain was being stolen, sold on the black market and not getting to those in need.

Why should I even bother trying to apply a Malthusian model to Ethiopia (ETH) when Nobel Laureate William Nordhaus and most of the Economics profession argue that a Neoclassical General Equilibrium model (the DICE model) apples to every region of the World-System and, supposedly, to every country in the World-System. Critics will argue that I am just trying to push the conventional Malthusian policy conclusion: Ignore the poor and hungry because feeding them will just increase their birth rate and further increase population pressure.

World-Systems Theory (WST) has an answer to the question of what is the appropriate model to apply to a particular country: It depends on the country's place in the hierarchical structure of the World-System. Is it a Core, Semi-peripheral or Peripheral country? Core countries are mostly Capitalist, Semi-peripheral countries are Mixed with some elements of Capitalism and Peripheral countries are, I would argue, Malthusian-agricultural economies living on the edge of repeated food crisis and domination by core and semi-peripheral countries.* Most readers will understand what a Capitalist or Mixed economy is because they live in one. But what is a Malthusian economy?

Thomas Robert Malthus (1766-1834) was an English economist, cleric and scholar (political economy and demography). He predicted, controversially, that if population growth exceeded the productive capacity (carrying capacity) of the economy, a Malthusian Crisis would result, where "positive checks" such as famine, war, drought, immigration, etc. would reduce population pressure. Only "preventive checks" (birth control, delayed marriage, etc.) would prevent these catastrophes because population growth would, if uncontrolled, always exceed the productive capacity of the economy.

Famines have occurred periodically in the history of Ethiopia according to records dating to the 9th Century. To say why these famines happened and that they are definitely not the result of population pressure would be amazingly arrogant. And, to say that Neoclassical Economic Theory applies to all countries and to all recorded history would be equally arrogant. In fact, none of the modern models can be tested on Ethiopia because, aside from sparse World Bank data after WWII (the WDI or World Development Indicators), data is very weak for Ethiopia (although there is more data for regions in Africa but still not enough to test the regional DICE model).

Still, Karl Marx (1818-1883) called Malthus' population principle a "libel on the human race" and Malthus himself the "reverend scribbler." Indeed, "every schoolboy knows that Malthus was wrong" (Benjamin Higgins, 1968). Julian Simon (1932-1998) has argued that the World's carrying capacity is essentially unlimited. On the other hand, Jared Diamond has documented that the Rwanda Genocide was the result of population pressure. Why is Malthusian Theory so controversial and requires current analysts to keep writing Why Malthus Is Still Wrong. The continuing confusion involves failing to differentiate between the "Malthusian Model," the evidence supporting it, the "Malthusian Policy Recommendations" and the World-System. This particular Model-Evidence-Policy-System confusion, however, is true of every mental or formal model and is worth understanding for the well-documented and simple Malthusian Model.

The Malthusian Model (MM) is the model on which all other models are implicitly based (see Table I). Usually population growth is taken as exogenous because Capitalist economies can accommodate the demands of an expanding population. The original MM was simply two equations: a linear one for production growth, Q, and a geometric one for population growth, N. The equations didn't interact as a system** and when growth in N exceed Q, a Malthusian crisis was triggered. Kenneth Boulding put (Q,N) together in a system, with no assumptions about functional forms, and we have the modern version. The MM System model uses the state of the system S=(Q-N) as an Error-Correcting Controller (ECC); when (Q>N) population can expand (a feedback effect) and when (Q<N) population will contract through "positive checks".

Measuring Crisis

The MM Systems Model can be estimated for Ethiopia after WWII using the WDI to determine the state of the Malthusian Crisis. The first step is to estimate a measurement model using data we have from the WDI. N and Q are the most complete series and, luckily, form the basic Malthusian model.

 Measurement Matrix 

      N     Q

[1,]  0.707 0.707

[2,] -0.707 0.707

 Fraction of Variance 

[1] 0.958 1.000

The Measurement matrix can be estimated using Principal Components Analysis (PCA). The components will be used to form the approximate state variables of the Malthusian System. When estimated, the first component is overall growth (ETH1 = 0.707 N + 0.707 Q) and the second component, the Error Correcting Growth Controller (ETH2 = 0.707 Q - 0.707 N). Growth explains 96% of the variance and the ECC explains 4%.

The Figure above shows ETH1 (Growth) and ETH2 (The Malthusian ECC) plotted over time. ETH2 enters negative Malthusian-Criss territory around 1990 and starts recovering after 2010 (the 1983-1985 Famine was the worst in a Century and started the downward slide in the Malthusian Crisis). Overall growth (ETH1) although wiggling a little over time was not permanently affected.

Typically, commenting on historical time plots is as far as historical analysis gets, Malthusian or not. But I want to estimate a system model and try to understand how trends are causally related. 

Modeling Results

Modeling forces the question of "What is the System?" World Systems Theory (WST) provides a framework for answering the question. Ethiopia (ETH) is a country embedded with in a system of other countries. 

Discussion

NOTES

* My identification of Ethiopia as a Peripheral Country is a little casual and can be debated (see Babones, 2005). In studying the WDI, one indicator of Peripheral status is simply the lack of information in the data set. Semi-Peripheral and Core countries are fully populated with data.

** We might criticize Malthus for not inventing Systems Theory (a Twentieth Century discovery) and Marx came close recognizing that social systems are "over-determined" (Wolff and Resnick, 2006). You can read more Marx and Engels on the Population Bomb here. Unified Growth Theory puts all these various approaches together in one model starting with the MM at low levels of growth or stagnation (the Malthusian Trap) and ending with the Steady State Economy.

Appendix: ECC Models

Appendix: Systems Model

Models have a compact R-code in dse and can be run easily in Snippets. Note that the RUL20 model is only unstable in the feedback components $F[3,3] = 1.03$. If you stabilize the third feedback component (e.g.,$F[3,3] = 0.98$)  the entire system is stable. 

===========

merge.forecast <-

function (fx,n=1) {

#

# Merges a forecast with the output data

x <- splice(fx$pred,fx$forecast[[n]])

colnames(x) <- seriesNames(fx$data$output)

return(x)

}

#

#

# RUL20  Russia (1950-2000)

#

# Measurement Matrix 

#    EN.ATM.CO2E.KT EG.USE.COMM.KT.OE NY.GDP.MKTP.KD SL.TLF.TOTL.IN SP.POP.TOTL

#[1,]        0.28209            0.4060         0.3336         0.4343      0.3721

#[2,]       -0.43993           -0.2199        -0.1359         0.1328      0.2266

#[3,]        0.06433           -0.1446         0.5944         0.0494     -0.3944

#     SL.UEM.TOTL.ZS     HDI      EF    KOF

#[1,]         0.1893 0.43400  0.2348 0.1948

#[2,]         0.4971 0.03409 -0.3950 0.5161

#[3,]        -0.3374 0.22538 -0.4878 0.2470

#

 #Fraction of Variance 

#[1] 0.5489 0.8484 0.9677 0.9814 0.9921 0.9975 0.9988 0.9995 1.0000

require(dse)

require(matlab)

AIC <- function(model) {informationTestsCalculations(model)[3]}

f <- matrix( c( 0.976658001, 0.02127754,  0.2249071, 0.161990376,

                     -0.008392259, 0.97543675, -0.2319674, 0.001666581,

                     -0.005587383, 0.09718186,  1.0312754, 0.035854885,

                      0.000000000, 0.00000000,  0.0000000, 1.000000000

),byrow=TRUE,nrow=4,ncol=4)

h <- eye(3,4)

k <- f[1:4,1:3,drop=FALSE]

RUL20 <- SS(F=f,H=h,K=k,

z0=c(0.161990376, 0.001666581, 0.035854885, 1.00000000),

              output.names=c("RU1","RU2","RU3"))

stability(RUL20)

#tfplot(simulate(RUL20,sampleT=20))

shockDecomposition(toSSChol(RUL20))

RUL20.data <- simulate(RUL20,sampleT=50,start=1950,noise=matrix(0,50,3))

m <- l(RUL20,RUL20.data)

#tfplot(m)

AIC(m)

tfplot(RUL20.f <- forecast(m,horizon=50))

RUL20.fx <- merge.forecast(RUL20.f)

#    Models have a compact R-code in dse and can be run easily in Snippets. 

#    The RU20 must be run first to provide input for #ETH20.

#

# W20 ETH (Ethiopia) Russia Input

#

# Measurement Matrix 

#       N  Q

#[1,]  0.707 0.707

#[2,] -0.707 0.707

#

#Fraction of Variance 

#[1] 0.958 1.000

#

require(dse)

require(matlab)

AIC <- function(model) {informationTestsCalculations(model)[3]}

f <- matrix( c(  1.04647269, -0.1059723, 0.10155553,

                        0.01918655,  0.9306230, 0.01335861,

                  0.000000000,  0.00000000,  1.00000000

),byrow=TRUE,nrow=3,ncol=3)

g <- matrix(c(-0.003819938, -0.01406381, 0.009235749,

                     -0.010773904, -0.01627134, 0.017135870,

                      0.000000000 , 0.00000000, 0.000000000

),byrow=TRUE,nrow=3,ncol=3)                      

h <- eye(2,3)

k <- f[1:3,1:2,drop=FALSE]

ETH20 <- SS(F=f,H=h,K=k,z0=c(0.11991149, 0.04457381, 1.00000000),

              output.names=c("Growth","(Q-N)"))

stability(ETH20)

shockDecomposition(toSSChol(ETH20))

ETH20.data <- simulate(ETH20,sampleT=50,start=1950,noise=matrix(0,50,2))

m <- l(ETH20,ETH20.data)

#tfplot(m)

AIC(m)

tfplot(forecast(m,horizon=50))

ETH20x <- SS(F=f,H=h,K=k,G=g,z0=c(0.11991149, 0.04457381, 1.00000000),

              output.names=c("Growth","(Q-N)"))

ETH20x

data <- TSdata(output=outputData(ETH20.data),input=RUL20.fx)

m <- l(ETH20x,data)

#tfplot(m)

AIC(m)

shockDecomposition(m)

tfplot(forecast(m,horizon=50,conditioning.inputs=RUL20.fx))